Finite Group Databasebeta

← Group #152176

Character table — Group #152176

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11222222222222244444444444448888888888888888888888161616161616161632323232
order12222444488161616162244888161616161616881616161632323232323232323232323232323232222222444488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ6111111111111111-1-1-1-1111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ7111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ8111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ9111-1-11-11-111-1-1-1-11-11-11-1-11111-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11-11-1i−ii−i
χ10111-1-11-11-111-1-1-1-11-11-11-1-11111-1-11-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-11-11−ii−ii
χ11111-1-11-11-111-1-1-1-11-11-11-1-11111-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11-11-1−ii−ii
χ12111-1-11-11-111-1-1-1-11-11-11-1-11111-1-11-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-11-11i−ii−i
χ13111-1-11-11-111-1-1-1-1-11-111-1-11111-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-11-11i−i−ii
χ14111-1-11-11-111-1-1-1-1-11-111-1-11111-1-1-11-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1111-11-1−iii−i
χ15111-1-11-11-111-1-1-1-1-11-111-1-11111-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11-11−iii−i
χ16111-1-11-11-111-1-1-1-1-11-111-1-11111-1-1-11-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1111-11-1i−i−ii
χ1722222222222-2-2-2-22222222-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ1822222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ19222222222-2-200002222-2-2-2000000-2-2000022−2−222−2−222−2−222−2−2000000000000
χ20222222222-2-200002222-2-2-2000000-2-20000−2−222−2−222−2−222−2−222000000000000
χ21222222222-2-20000-2-2-2-2-2-2-200000022000022−2−222−2−2−2−222−2−222000000000000
χ22222222222-2-20000-2-2-2-2-2-2-2000000220000−2−222−2−22222−2−222−2−2000000000000
χ23222-2-22-22-22222222-22-22-2-2-2-2-2-2222-2-2-2220000000000000000000000000000
χ24222-2-22-22-2222222-22-222-2-2-2-2-2-222-2222-2-20000000000000000000000000000
χ25222-2-22-22-2-2-200002-22-2-222000000-220000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2000000000000
χ26222-2-22-22-2-2-200002-22-2-222000000-220000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2000000000000
χ27222-2-22-22-2-2-20000-22-22-2220000002-20000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2000000000000
χ28222-2-22-22-2-2-20000-22-22-2220000002-20000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2000000000000
χ2922-22-222-2-20022−2−222-2-200022−2−22−2002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ3022-22-222-2-20022−2−222-2-200022−2−22−2002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ3122-22-222-2-20022−2−2-2-22200022−2−22−200−22−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5000000000000
χ3222-22-222-2-20022−2−2-2-22200022−2−22−200−22−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5000000000000
χ3322-22-222-2-200−2−22222-2-2000−2−222−2200−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ3422-22-222-2-200−2−22222-2-2000−2−222−2200−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ3522-22-222-2-200−2−222-2-222000−2−222−22002−22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7000000000000
χ3622-22-222-2-200−2−222-2-222000−2−222−22002−22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7000000000000
χ3722-22-2-2-2222222220000-22-22-22-2-2-20000000000000000000000000022-2-20000
χ3822-22-2-2-2222222220000-22-22-22-2-2-200000000000000000000000000-2-2220000
χ3922-22-2-2-22222-2-2-2-20000-22-2-22-222200000000000000000000002-22-200000000
χ4022-22-2-2-22222-2-2-2-20000-22-2-22-22220000000000000000000000-22-2200000000
χ4122-2-222-2-220022−2−22-2-22000−2−2222−200−222−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ4222-2-222-2-220022−2−22-2-22000−2−2222−200−222−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ4322-2-222-2-220022−2−2-222-2000−2−2222−2002−2−22ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5000000000000
χ4422-2-222-2-220022−2−2-222-2000−2−2222−2002−2−22−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5000000000000
χ4522-2-222-2-2200−2−2222-2-2200022−2−2−22002−2−22ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ4622-2-222-2-2200−2−2222-2-2200022−2−2−22002−2−22−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ4722-2-222-2-2200−2−222-222-200022−2−2−2200−222−2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7000000000000
χ4822-2-222-2-2200−2−222-222-200022−2−2−2200−222−2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7000000000000
χ4922-2-22-222-22222220000-2-22-22-22-2-200000000000000000000002-2-2200000000
χ5022-2-22-222-22222220000-2-22-22-22-2-20000000000000000000000-222-200000000
χ5122-2-22-222-222-2-2-2-20000-2-222-22-222000000000000000000000000002-2-220000
χ5222-2-22-222-222-2-2-2-20000-2-222-22-22200000000000000000000000000-222-20000
χ5344444-4-4-4-4002222−22−22000000022−22−2222−22220000000000000000000000000000000000
χ5444444-4-4-4-400−22−2222220000000−222222−2222−220000000000000000000000000000000000
χ55444-4-4-44-44002222−22−220000000−222222−22−22220000000000000000000000000000000000
χ56444-4-4-44-4400−22−222222000000022−22−222222−220000000000000000000000000000000000
χ5744-44-4-4-444-4-4000000004-440000000000000000000000000000000000000000
χ5844-4-44-444-4-4-40000000044-40000000000000000000000000000000000000000
χ598-8000000042−424ζ−4ζ7−4ζ+4ζ74ζ3−4ζ5−4ζ3+4ζ500000000000000000000000000000000000000000000000
χ608-8000000042−42−4ζ+4ζ74ζ−4ζ7−4ζ3+4ζ54ζ3−4ζ500000000000000000000000000000000000000000000000
χ618-80000000−42424ζ3−4ζ5−4ζ3+4ζ5−4ζ+4ζ74ζ−4ζ700000000000000000000000000000000000000000000000
χ628-80000000−4242−4ζ3+4ζ54ζ3−4ζ54ζ−4ζ7−4ζ+4ζ700000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.